UNIVERSITY OF CALIFORNIA, SAN DIEGO. of the Cat. of Philosophy. in Neurosciences. Paul Bush

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1 UNIVERSITY OF CALIFORNIA, SAN DIEGO Compartmental Models of Single Cells and Small Networks in the Primary Visual Cortex of the Cat A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Neurosciences by Paul Bush Committee in charge: Professor Terrence J. Sejnowski, Chair Professor Patricia S. Churchland Professor Allen Selverston Professor Thomas D. Albright Professor Martin I. Sereno 1995

2 The dissertation of Paul Bush is approved, and it is acceptable in quality and form for publication on microfilm: Chair University of California, San Diego 1995 iii

3 TABLE OF CONTENTS Signature Page... Table of Contents... List of Figures and Tables... Acknowledgements... Vita and Publications... iii iv v viii x Abstract... xiii I Introduction... 1 II Effects of Inhibition and Dendritic Saturation in Simulated Neocortical Pyramidal Cells III Reduced Compartmental Models of Neocortical Pyramidal Cells IV Synchronization of Bursting Action Potential Discharge in a Model Network of Neocortical Neurons V Inhibition Synchronizes Sparsely Connected Cortical Neurons Within and Between Columns in Realistic Network Models iv

4 LIST OF FIGURES AND TABLES II.1 Drawings of reconstructed HRP-filled layer 2 (right) and layer 5 (left) pyramidal cells 48 II.2 Simulation of reduction in amplitude of EPSP by synaptic activity 49 II.3 Dendritic saturation during physiological synaptic activation 50 II.4 Effect of inhibition on dendritic saturation at low input rates 51 II.5 Effect of inhibition on firing rate of synaptically activated model layer 2 pyramid 52 II.6 Decrease in input resistance of model layer 2 pyramidal cell during synaptic activation 53 II.T1 Parameters for active conductances 54 II.T2 Percentage decrease in Rin during concurrent synaptic excitation and inhibition 55 III.1 Drawings of reconstructed HRP-filled layer 2 (right) and layer 5 (left) pyramidal cells 73 III.2 Comparison of the response of the reduced (R) and full (F) models to somatic input 74 III.3 Comparison of firing responses of reduced and full model layer 5 pyramidal cell 75 III.T1 Dimensions of reduced models 76 v

5 IV.1 Reconstructed and model layer 5 pyramidal cell with cortical network 90 IV.2 Response of partially connected model network to constant thalamic input 91 IV.3 Response of fully connected model network to constant thalamic input 92 IV.4 Synchronization is not dependent on identical, constant thalamic input 93 IV.T1 Model parameters 94 V.1 Intrinsic firing properties of isolated model neurons 131 V.2 Activity in models of 100 isolated layer 5 cortical neurons 132 V.3 Intracolumnar synchronization in a model network of neurons connected with a probability of 10% 133 V.4 Synchronization of a 1000 neuron network connected at a density of 5% 134 V.5 Higher resolution plot of the membrane potential of the 4th pyramidal cell from Fig V.6 The response of a simple cell recorded intracellularly in area 17 of the cat 136 V.7 Effect of increasing the strength of reciprocal inhibition between the basket cells in a 100 neuron network 137 vi

6 V.8 Zero phase lag synchrony between two columns of 100 neurons 138 V.9 Cross-correlations of the LAPs of twocolumn simulations 139 V.10 Phase difference between LAPs from twocolumn simulations 140 V.11 Synchrony between columns is severely degraded by increasing the inter-columnar time delay 141 V.12 Response of a sample basket cell and two representative pyramidal cells to stimulation of inter-columnar connections 142 V.13 Inter-columnar connections have little effect on an undriven column 143 vii

7 ACKNOWLEDGEMENTS Firstly, I wish to thank Terry Sejnowski. He has provided me with six years of continuous support and understanding; people who know me well will appreciate this. With his vast spectrum of knowledge, extremely fast comprehension and insight combined with years of wisdom, Terry s supervision has of course been invaluable during the course of my studies. I am also grateful to the many members of CNL both past and present. The many lab meetings, journal clubs and discussions I have had with people too numerous to mention individually have lead to direct developments of and improvements to my work, but also, and probably more importantly, the way in which I think about my work has been developed and improved by interactions with the eclectic group of people that is CNL. In addition, I would like to express my gratitude to Rosemary Miller, whose generous help over the years has contributed to making my time at the Salk enjoyable and as stress-free as possible. Periodic discussions and collaborations with Rodney Douglas and Kevan Martin, my first mentors, have formed an integral part of my thesis work and I look forward to continuing associations in the future. I am indebted to them for advising me to come to San Diego and arranging for me to meet and work for Terry Sejnowski. Finally, I thank Rita Venturini. Besides enriching my life over the last few years she has provided much appreciated support and encouragement when it was most needed. Chapter 2, in full, is a reprint of the material as it appears in Journal of Neurophysiology, 71(6): , It was written in collaboration with T.J. Sejnowski. The dissertation author was the primary investigator of this paper. We thank R.J. Douglas and K.A.C. Martin for providing us with the cortical cell morphologies, Idan Segev for comments on the manuscript and D. Ferster for a number of useful discussions. viii

8 Support was provided by The Howard Hughes Medical Institute and The National Institute for Mental Health. Chapter 3, in full, is a reprint of the material as it appears in Journal of Neuroscience Methods, 46: , It was written in collaboration with T.J. Sejnowski. The dissertation author was the primary investigator of this paper. Chapter 4, in full, is a reprint of the material as it appears in Neural Computation, 3:19-30 (1991). It was written in collaboration with R.J. Douglas. The dissertation author was the primary investigator of this paper. We thank John Anderson for technical assistance. PCB acknowledges the support of the McDonnell-Pew Foundation. RJD acknowledges the support of the Mellon Foundation and the SA MRC. ix

9 VITA January 2, 1967 Born, Birmingham, England Research project for M.R.C. A.N.U., Oxford, U.K B.A. Neurophysiology & Psychology, University College, Oxford, U.K Awarded Fulbright Scholarship for graduate study in U.S Attended 'Methods in Computational Neuroscience' MBL course, Wood's Hole, MA Neurosciences graduate student, UCSD. Advisor: T.J. Sejnowski, Salk Institute. 1992, 1993 Teaching Assistant, Departments of Psychology and Biology, UCSD. 1990, 1994 Awarded McDonnell-Pew travel grants for research collaboration PhD University of California, San Diego. PUBLICATIONS Berman, N. J., Bush, P. C. & Douglas, R. J. Adaptation and bursting in neocortical neurons may be controlled by a single fast potassium conductance. Quarterly Journal of Experimental Physiology. 74: , Bush, P. C. and Douglas, R. J. Synchronization of bursting action potential discharge in a model network of neocortical neurons. Neural Computation. 3: 19-30, x

10 Bush, P. C. and Sejnowski, T. J. Simulations of a reconstructed Cerebellar Purkinje Cell based on simplified channel kinetics. Neural Computation. 3: , Bush, P. C. and Sejnowski, T. J. Reduced compartmental models of neocortical pyramidal cells. Journal of Neuroscience Methods. 46: , 1993 Bush, P. C. and Sejnowski, T. J. Effects of inhibition and dendritic saturation in simulated neocortical pyramidal cells. Journal of Neurophysiology. 71:6, Bush, P. C. and Sejnowski, T. J. Inhibition synchronizes sparsely connected cortical neurons within and between columns in realistic network models. Journal of Computational Neuroscience 1995 (submitted for publication). ABSTRACTS Bush, P. C. & Sejnowski, T. J. Large-scale compartment model of a cerebellar Purkinje cell. Neuroscience Abstracts. 16, 1298, Bush, P. C., Li, S. & Sejnowski, T. J. Quantal analysis of superimposed EPSPs from multiple synapses. Neuroscience Abstracts. 17, 385, Bonds, A. B., Snider, R. K., Kabara. J., Bush, P. and Sejnowski, T. J. On the origins of oscillation in cells of the cat striate cortex.. ARVO. 34/ Bush, P. C., Gray, C. & Sejnowski, T. J. Realistic simulations of synchronization in networks of layer V neurons in cat primary visual cortex. Neuroscience Abstracts.: 1993 INVITED TALKS The use of reduced compartmental models in cortical network simulations. In: Chicago Workshop on Computational Neuroscience: Models of Thalamic and Cortical Neurons BOOK CHAPTERS xi

11 Bush, P. C. & Sejnowski, T.J. Simulations of synaptic integration in neocortical pyramidal cells. In:Computation and Neural Systems.. Eds. F. H. Eeckman & J. M. Bower. Kluwer, Boston Bush, P. & Sejnowski, T. Models of Cortical Networks. In: Normal and Pathophysiological Physiology of The Cortical Neuron. Eds. I. Mody & M. Gutnik. Oxford Univ. Press xii

12 ABSTRACT OF THE DISSERTATION Compartmental Models of Single Cells and Small Networks in the Primary Visual Cortex of the Cat by Paul Bush Doctor of Philosophy in Neurosciences University of California, San Diego, 1995 Professor Terrence J. Sejnowski, Chair This thesis has two main themes. Firstly it documents the process of constructing realistic single cell and network models, focusing particularly on how to represent individual neurons in network models consisting of hundreds to thousands of units. In the third chapter a method of drastically reducing the number of compartments in a single cell model is presented. The method is based on conserving the axial resistance of the model neuron and not the surface area. The resulting reduced model neuron displays the same electrotonic characteristics as the original full-size model neuron while taking up a fraction of the memory and computation time. In addition the reduced model neuron retains the spatial dimensions of the full model, an important consideration when attempting to construct spatially accurate models of laminar cortical areas. Secondly, the subject of cortical inhibition is addressed. In the last few years the perception of the role of inhibition in the neocortex has changed from that of a powerful xiii

13 antagonist of non-specific excitation to that of a synergistic process helping to shape the excitatory response. The second chapter presents results from a single cell simulation of a recent experiment, showing how excitatory and inhibitory synaptic inputs interact non-linearly in a neuron s dendritic tree. It also demonstrates that while cortical inhibition may be strong enough to suppress even strongly excited cells, it does not do so in the sustained manner necessary to veto non-specific excitation. The forth and fifth chapters show how strong inhibition can have a role in cortical dynamics when activated transiently by a synchronized burst of pyramidal cell firing. The brief but powerful inhibitory activity serves to truncate and demarcate the burst of firing in the pyramidal cell population. In this manner the inhibition is essential for producing synchronized oscillatory activity in the network. In this system inhibition is maximally active during the period that excitation is greatest, but inhibition and excitation function together rather than in opposition. In addition, the properties and characteristics of synchronized oscillatory activity both within and between cortical columns are analyzed in these chapters. xiv

14 CHAPTER I Introduction The perspective of a computational neuroscientist What does the neocortex do? We know the answer to this, the neocortex does us. In all probability it is the part of the brain most responsible for generating what we think of as ourselves, our humanness. How does the neocortex function? What are some basic principles of cortical neuronal operation? At the fundamental level of single cells and microcircuits consisting of hundreds to thousands of cells, we really have no answers to these questions at the present time. A significant amount of work has been done at the single cell level discovering and analyzing the cable properties of neurons, characterizing the electrotonic spread of current and documenting a plethora of ligand- and voltage-gated conductances (Rall 1964; Hille 1984; McCormick 1989). The results of this work are of course essential for developing an understanding of, but do not directly address, how single cortical cells operate and what function they are performing. In part this is because it is very difficult if not impossible to determine the function and role of single cells just by studying single cells. After characterizing their basic intrinsic properties the cells must be studied in the context of the circuits that they make up. The functions and principles of 1

15 2 operation of single cortical cells and small networks of such cells will most likely be discovered together. Single cells have features and properties whose purposes will only become clear when considered in their appropriate roles in the network, just as networks of cells will show behaviors and exhibit phenomena that depend on particular characteristics of their component cells. What is the best way to discover how cortex operates, the fundamental principles? A great deal of experimental work has been done on cortex; anatomy and physiology of networks as well as single cell studies. This work provides constraints within which any comprehensive understanding or theory of cortex must fit. It can also provide some clues as to how the cortex must operate; we now know that all neocortex from primary sensory to frontal association cortex, from rat to human cortex, is organized along similar lines (Martin 1988). Thus, whatever the task, each area of cortex uses the same basic circuit to accomplish it - the biggest difference is the source of the inputs. The following facts are general features of all neocortex: The primary input enters the middle layers, is relayed to the upper layers and then to the deeper layers. The upper layers project to other cortical areas and the lower layers project out of cortex and back to the origin of the inputs. Most cortical neurons are excitatory and are covered in spines, they are the projection neurons of cortex. Approximately 20% of cortical neurons are inhibitory and are not very spiny, they are the interneurons. Recent work shows that the excitatory projection neurons also make significant contributions to the intrinsic circuitry of cortex, and the details of this circuitry are beginning to be mapped out (see Douglas and Martin (1990b) for review). However, these data, synthesized into principles of organization, are not principles of function. It is unlikely that principles of function at the level of the cortical microcircuit - how a cortical column operates, beginning with its dynamics - can be divined just from consideration of the data. The main reason for this is that cortical circuitry is so complex and consists of many feedback loops. Consider, for example, the first few synapses in the

16 3 primary visual cortex of the cat, focusing just on the features that are likely to be general properties of neocortex. The spiny stellate cells in layer 4 receive a numerically small input from the thalamus, a much larger input comes from the neighboring (200 µm) layer 4 spiny stellates in the same column. The thalamic input also activates layer 4 inhibitory cells which contact the spiny stellates. The spiny stellates in turn contact the inhibitory cells, and the inhibitory cells contact each other. However, the largest input to the spiny stellates is from pyramidal cells of layer 6 which contact layer 4 spiny stellates and inhibitory neurons over a wide area (up to 1mm). These layer 6 cells also receive direct input from the thalamus and project back to the precise area from which they receive input. A portion of their dendritic tree arborises over a wide area in layer 4 (~500 µm) where it can receive inputs from spiny stellate cells, inhibitory interneurons, thalamic afferents and possibly other layer 6 cells (Ahmed et al. 1994). A consideration of this anatomy is daunting enough for someone interested in how layer 4 responds to thalamic input, but there is also the physiology to consider. Spiny stellates and layer 6 pyramids fire relatively low frequency adapting trains of action potentials while inhibitory interneurons such as those of layer 4 (clutch cells) have low thresholds and fire high frequency non-adapting trains of short duration spikes (McCormick et al. 1985). Layer 6 cells are particularly sensitive to modulatory neurotransmitters such as noradrenalin and acetylcholine which cause dramatic changes (increases) in response rates (Singer et al. 1976). These modulatory systems are not very active under the anesthetized conditions of most in vivo experiments. In order to understand exactly how layer 4 (the gateway to cortex) functions, all these facts must be considered together. Consider just the case of an excitatory projection that terminates on both excitatory and inhibitory neurons in its target area, a common feature of neocortex. What is the function of this projection? Is it excitatory or inhibitory? A definitive answer cannot be given without knowing the intrinsic properties of the input and target cells as well as,

17 4 and this is crucial, the current state of the network. If the target cells are relatively hyperpolarized then the lower threshold inhibitory neurons will fire first and prevent any activity building up in the excitatory cells. If the target cells are depolarized by other synaptic activity then the excitatory cells, containing sub-threshold voltage-dependent conductances activated by depolarization, will fire in response to the input and activity will begin to build up in the target population (Hirsch and Gilbert 1991). So the state of all of the components of the cortical circuit at any time is a major determinant of its response to input. Returning to the case of layer 4 we see that it is difficult if not impossible to say what the output will be to any input just by considering the (extremely complex) anatomy and physiology. Somehow we need to incorporate all that data and at the same time keep track of the state of all the components in the circuit as the response develops. The most effective way of doing this at present is with computer simulation. All the anatomical data and intrinsic physiological properties can be included in accurate representations of neurons and their synaptic connections. The states of every component are updated as the simulation is numerically integrated. Ideally, one can just watch the results appear - if your model is accurate you discover how layer 4 responds to input just by watching the simulation progress. Of course in practice things are not so simple. Firstly, the simulation is completely dependent on the data put into it. There must be enough reliable data to constrain the model, if any parameters have to be estimated then it must be shown that the results of the simulation are not affected by variations in these parameters. Constraining simulations with experimental data is the biggest problem to overcome when doing realistic models of the brain. Many brains systems cannot yet be realistically modeled because sufficient data does not yet exist. Only in the last few years has sufficient data become available (and computers become powerful enough) to attempt realistic cellular models of primary visual cortex.

18 5 Secondly, the model neurons and synapses must be accurate representations of the known experimental data. Fortunately cable theory (Rall 1964) and Hodgkin Huxley voltage-dependent conductance dynamics (Hodgkin and Huxley 1952) have been proven to provide robust descriptions of single neuron synaptic integration and active responses. These systems of equations have been incorporated into a simulation package known as NEURON (Hines 1989), which through its various incarnations has been the simulator I have used for most the simulations presented in this thesis. Beyond the single neuron level there are other issues of accuracy in representation to be considered. Once such issue, forced on us by the limits of computer power, is how to represent single cells in network simulations containing hundreds or thousands of units. The large compartmental models used for single cell studies take up too much memory and run too slowly, as well as being simply to unwieldy for convenient use in network simulations. The third chapter in this thesis addresses this issue, introducing a technique to drastically reduce the complexity of compartmental neuron representations while preserving their essential electrotonic properties. The common theme running through the other three chapters (I have to thank my supervisor, Terry Sejnowski, for steering me in this direction) is the role of inhibition in cortex. The prevalent view of the role of cortical inhibition until very recently was as a negator or veto of inappropriate, broadly tuned excitation (Martin 1988). As well as seeming intuitively quite reasonable, this theory appeared to be supported by strong experimental evidence (Sillito 1975). However, later experimental and theoretical work challenged the assumption that cortical stimulus selectivity is based on strong inhibition of inappropriate excitation (Douglas et al. 1988; Koch et al. 1990; Ferster 1986) and even suggested that inhibition in cortex is not strong enough to suppress neurons receiving strong excitatory input (Douglas and Martin 1990a). In Chapter 2 the effect and strength of inhibition is assessed in single cell simulations based on experiment. It is shown that

19 6 although strong and effective inhibition can be evoked during physiological synaptic stimulation, such inhibition must be transient and not responsible for sustained inhibition of excitatory input. Chapters 3 and 4 investigate a paradigm in which such strong, transient inhibition not only occurs but creates the characteristic network dynamics. This paradigm is synchronized oscillatory activity, a phenomenon observed in a wide range of experimental preparations (Singer 1993) and the subject of significant speculation as to its role (Crick and Koch 1990). The work presented here is a beginning in the field of realistic modeling of cortical microcircuitry. It has involved itself in one of the fundamental principles of cortical circuitry operation; the role of inhibition. However, it is only a starting point, and even a full model of a cortical column of this type would not provide all the answers as to how a canonical cortical microcircuit functions. This is because the type of model I have worked on to date does not include learning or plasticity. Cortical circuitry is not static, the synaptic strengths and perhaps the physical connections constantly change as the cortex does its job. Once the basic properties of a cortical microcircuit have been established it is most likely that the circuit will have to be considered in the context of learning and change in order for us to be able to fully understand its function. Studying the static circuit is equivalent to studying the single cell in isolation - an essential step but it cannot lead to a comprehensive theory of cortex.

20 7 References Ahmed, B., Anderson, J. C., Douglas, R. J., Martin, K. A. C., and Nelson, C. J. Polyneuronal innervation of spiny stellate neurons in cat visual cortex. (1994) J. Comp. Neurol., 341: Crick, F., and Koch, C. Towards a neurobiological theory of consciousness. (1990) Sem. Neurosci., 2: Douglas, R. J., and Martin, K. A. C. Control of neuronal output by inhibition at the axon initial segment. (1990a) Neural Comp., 2: Douglas, R. J., and Martin, K. A. C. (1990b) Neocortex. In: Synaptic Organization of the Brain G. Shepherd (Ed.), New York: Oxford University Press. p Douglas, R. J., Martin, K. A. C., and Whitteridge, D. Selective responses of visual cortical cells do not depend on shunting inhibition. (1988) Nature, 332: Ferster, D. Orientation selectivity of synaptic potentials in neurons of cat primary visual cortex. (1986) J. Neurosci., 6: Hille, B. (1984) Ionic Channels of Excitable Membranes. Sunderland, MA: Sinauer Associates, Inc. Hines, M. L. A program for simulation of nerve equations with branching geometries. (1989) Int. J. Biomed. Comp., 24: Hirsch, J. A., and Gilbert, C. D. Synaptic physiology of horizontal connections in the cat's visual cortex. (1991) J. Neurosci., 11: Hodgkin, A. L., and Huxley, A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. (1952) J. Physiol., 117: Koch, C., Douglas, R., and Wehmeier, U. Visibility of synaptically induced conductance changes: theory and simulations of anatomically characterized cortical pyramidal cells. (1990) J. Neurosci., 10: Martin, K. A. C. From single cells to simple circuits in the cerebral cortex. (1988) Q. J. Exp. Physiol., 73: McCormick, D. A. GABA as an inhibitory neurotransmitter in human cerebral cortex. (1989) J. Neurophysiol., 62:

21 8 McCormick, D. A., Connors, B. W., Lighthall, J. W., and Prince, D. A. Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex. (1985) J. Neurophysiol., 54: Rall, W. (1964) Theoretical significance of dendritic trees for neuronal input-output relations. In: Neural Theory and Modeling R. Reiss (Ed.), Stanford: Stanford University Press. p Sillito, A. M. The contribution of inhibitory mechanisms to the receptive field properties of neurones in the striate cortex of the cat. (1975) J. Physiol., 250: Singer, W. Synchronization of cortical activity and its putative role in information processing and learning. (1993) Ann. Rev. Physiol., 55: Singer, W., Tretter, F., and Cynader, M. The effect of reticular stimulation on spontaneous and evoked activity in the cat visual cortex. (1976) Brain. Res., 102:

22 CHAPTER II Effects of Inhibition and Dendritic Saturation in Simulated Neocortical Pyramidal Cells Summary and Conclusions 1. We have used compartmental models of reconstructed pyramidal neurons from layers 2 and 5 of cat visual cortex to investigate the nonlinear summation of excitatory synaptic input and the effectiveness of inhibitory input in countering this excitation. 2. In simulations that match the conditions of a recent experiment (Ferster & Jagadeesh, 1992), dendritic saturation was significant for physiological levels of synaptic activation: A compound excitatory postsynaptic potential (EPSP) electrically evoked during a depolarization caused by physiological synaptic activation was decreased by up to 80% compared to an EPSP evoked at rest. 3. Synaptic inhibition must be coactivated with excitation to quantitatively match the experimental results. The experimentally observed coactivation of inhibition with excitation produced additional current shunts that amplified the decrease in test EPSP amplitude. About 30% of the experimentally-observed decrease in EPSP amplitude was 11

23 10 caused by decreases in input resistance (R in ) due to synaptic conductance changes; a reduced driving force accounted for the remaining decrease. 4. The amount of inhibition was then increased by nearly an order of magnitude, to about 10% of the total number of inhibitory synapses on a typical cortical pyramidal cell. The sustained firing of this many inhibitory inputs was sufficient to completely suppress the firing of a neuron receiving strong excitatory input. However, this level of inhibition produced a very large reduction in Rin. Such large reductions in Rin have not been observed experimentally, suggesting that inhibition in cortex does not act to veto (shunt) strong, sustained excitatory input (of order 100 ms). 5. We propose instead that strong, transient activation (< 10 ms) of a neuron's inhibitory inputs, sufficient to briefly prevent firing, is used to shape the temporal structure of the cell's output spike train. Specifically, cortical inhibition may serve to synchronize the firing of groups of pyramidal cells during optimal stimulation. Introduction The traditional function assigned to inhibition in cortex is to oppose excitation, acting to veto or shape the response of cortical cells by negating inappropriate excitation (Koch et al., 1987). Evidence for this view was provided by blocking inhibition with bicuculine and observing a decrease in the response selectivity of cortical neurons (Sillito, 1975). However, theoretical studies (Koch et al., 1990) have shown that inhibition strong enough to veto (shunt) significant amounts of excitatory current should produce measurable decreases in R in of the neuron in question. Such decreases in R in have never been seen in vivo when cortical neurons do not respond to non-preferred stimuli (Berman et al., 1991; Douglas et al., 1988), and electrically-evoked thalamocortical EPSPs are not

24 11 reduced in amplitude during visual stimulation at the nonpreferred orientation (Ferster & Jagadeesh, 1992). These results have led to the conclusion that cortical neurons receive neither excitatory nor inhibitory input in response to non-preferred stimuli (Berman et al., 1991). This conclusion is supported by results showing that both the excitation and the inhibition that a cortical neuron receives are tuned to the preferred orientation (Ferster, 1986). Thus it is becoming clear that the role of cortical inhibition is more complex than a veto of sustained, untuned excitation. A number of other functions for inhibition have been proposed: Recent physiological experiments using dual gratings (Bonds, 1989) have suggested that a general, non-selective inhibition acts as to normalize cortical responses. This idea receives direct anatomical support from the recent demonstration that large basket cells send (inhibitory) inputs to regions representing all orientaions, not just iso- or cross-orientations (Kisvardy & Eysel, 1993). Douglas and Martin have proposed that cortical inhibition acts to increase the threshold of target neurons and gate intracortical reexcitation (Douglas & Martin, 1992). In order to remain in a state that is sensitive to inputs, the excitation and inhibition to a cortical cell should be balanced (Bell, Mainen & Sejnowski (unpublished data)). In order to study these issues we have simulated a recent experiment (Ferster and Jagadeesh 1992) that used in vivo whole cell patch recording of neocortical neurons to study interactions between synaptic inputs. We have applied a compartmental model to the data of Ferster and Jagadeesh (1992) and shown that they are consistent with nonlinear interactions occurring in dendrites between excitatory inputs alone and between excitatory and inhibitory inputs. The same model was then used to determine conditions under which inhibition can prevent the firing of a neuron receiving synaptic excitation that is strong enough to cause it to discharge at high rates, and how much R in would change under these conditions. Our results, consistent with the experimental data, lead to a hypothesis in

25 12 which inhibition is strongly activated during periods of maximum excitation, yet not in a manner that causes a suppression of the firing response. Methods Simulations were performed using standard techniques for compartmental models of branching dendritic trees (Rall, 1964); two digitized HRP-filled pyramidal cells from layers 2 and 5 of cat visual cortex (Koch et al., 1990) were modeled (Fig. 1), each having approximately 400 coupled cylindrical compartments containing only resistive and capacitative elements. The simulator CABLE (Hines, 1989), running on a MIPS Magnum 3000/33, required about 1 minute of computation to simulate 100 ms of real time. Passive parameters Appropriate values of the passive parameters (specific membrane resistance, R m, specific membrane capacitance, C m, and specific axial resistance, R i ) were selected: C m for neuronal membrane has a long-established value of 1 µf/cm 2 (Jack et al., 1975). The accepted value of R i, at least in the mammalian central nervous system, has recently been revised upwards from its traditional value of about 70 Ωcm for a number of reasons: 1) Voltage responses to brief current pulses could not be modeled accurately with a small R i (Segev et al., 1992; Shelton, 1985; Stratford et al., 1989). 2) When modeling cerebellar Purkinje cells, a larger R i was necessary to produce significant attenuation of action potentials as they invade the dendritic tree (Bush & Sejnowski, 1991) 3) A large R i was needed to explain the observed somatic to dendritic input conductance ratio and steady-

26 13 state voltage attenuation of Purkinje cells (for a discussion of this issue see Shelton (1985)). The value chosen for R i in this study was 200 Ωcm (Bernander et al., 1991; Segev et al., 1992; Shelton, 1985; Stratford et al., 1989). Once R i, C m and the morphology have been fixed, the value chosen for R m will determine R in, the time constant, τ m, and the length constant, λ, of the cell. Recent results using whole-cell patch electrodes and Cs + -filled sharp electrodes have increased the estimate of R m from its traditional value of 5-10 kωcm 2 to a value of 50 to 100 kωcm 2 (Andersen et al., 1990; Major et al., 1990; Spruston & Johnston, 1992; Staley et al., 1992), giving R in s in the range of a GΩ. However, these results were not obtained in vivo, where the effect of background synaptic activity is such that a neuron with a R m of 100 kωcm 2 and can have an effective R in as low as 20 MΩ and an effective τ m of around 20 ms when part of an active in vivo circuit (Bernander et al., 1991; Rapp et al., 1992). The background synaptic input decreases the effective average R m of an in vivo neuron in a way that can be accurately taken into account by simply using a lower value for the effective R m in the model (Barrett & Crill, 1974; Bernander et al., 1991; Holmes & Woody, 1989). A sample of 25 visual cortical neurons recorded using sharp electrodes in vivo had R in s ranging from 10 to 153 MΩ (mean 69 MΩ) (Douglas et al., 1991). Two independent measurements of visual cortical neurons recorded using whole-cell patch electrodes in vivo had R in s ranging from 50 to 200 MΩ (Ferster & Jagadeesh, 1992) and 50 to 150 MΩ (Pei et al., 1991). The range of R in values reported by these studies are similar. Values for R in of 50 to 150 MΩ are closer to values obtained from the best sharp electrode in vitro recordings (Tanaka et al., 1991) than to the hundreds of MΩ obtained using whole-cell clamping in vitro. With a C m of 1 µf/cm 2 and R i of 200 Ωcm, we found that using a value of 20 kωcm 2 for R m produced R in s for the model layer 5 and layer 2 pyramidal cells of 45 MΩ and 110 MΩ, respectively. The layer 2 cell had a greater R in because it was smaller. With

27 14 these parameters (the standard model) both model cells have a dendritic τ m of 20 ms, which is a typical value for neocortical cells (Bernander et al., 1991). Though we believe that these values produce an accurate model of the in vivo neocortical pyramidal neuron, there is still considerable controversy surrounding "correct" values for the passive parameters R m and R i. Consequently, all simulations were repeated using values for R i of 70, 200 and 500 Ωcm and values for R m of 5, 20 and 100 kωcm 2. We focus on results obtained with the standard model (the default for all simulations), which we believe to be the most accurate fit to a functioning pyramidal cell, but we also present and discuss results obtained using the full range of values for R m and R i. In general we found only a quantitative, rather than a qualitative, difference between simulations using different parameter values, and none of our conclusions depend on precise values. Synaptic conductances EPSPs and inhibitory postsynaptic potentials (IPSPs) in our models were simulated as alpha function conductance changes with a peak amplitude of 0.5 ns and a time to peak of 1 ms. EPSPs had a reversal potential of 0 mv and IPSPs a reversal potential of -70 mv (Connors et al., 1988; McCormick, 1989). These parameters were chosen because they produced EPSPs at the soma with the same time course and amplitude as those observed experimentally (Mason et al., 1991; Thomson et al., 1988). Some simulations were done with synapses on explicitly modeled spines. In these cases we used the same 2- compartment model spine morphology as Qian and Sejnowski (1989), with spine neck dimensions 1 µm x 0.1 µm and head 0.69 µm x 0.3 µm. Trains of EPSPs or IPSPs were modeled according to a Poisson distribution with a mean frequency that is stated for each case. The resting membrane potential was -65 mv.

28 15 Active conductances For some simulations active conductances were placed at the soma to generate adapting trains of action potentials, as observed in regular-firing cortical neurons (McCormick et al., 1985). The action potential was mediated by fast sodium and potassium conductances (g Na + g Kd ). A high threshold calcium conductance (g Ca ), activated by each spike, introduced calcium into the cell. Intracellular calcium accumulated in the soma compartment and decayed exponentially to its resting value with a time constant of 20 ms (Traub et al., 1991). A slow calcium-sensitive potassium conductance (g Kca ) was included to produce the adaptation of firing rate. All the conductances used the Hodgkin-Huxley-like kinetics parameters developed by Borg-Graham (Borg-Graham, 1987), except for g Kca which had an activation rate equal to 200 times the intracellular calcium concentration (in ms -1 ) and a deactivation rate equal to the reciprocal of the activation rate. The implementation of our kinetic scheme follows that of Lytton and Sejnowski (1991). Briefly, each ionic current, I, was calculated from I = g m n h(v - E r ) (1) where g is maximal conductance, m is the activation variable, n is the exponent, h is the inactivation variable (g Na only), V is membrane potential and E r is the reversal potential of the ion concerned. The calcium current was calculated using the Goldman-Hodgkin-Katz equation (Hille, 1984), with g Ca the calcium permeability. The time- and voltagedependent variable, m, converged on a steady state value, m inf, given by m inf = α m /(α m +β m )

29 16 with a time constant, t m, given by t m = 1/(α m +β m ) The rate constants α m and β m were defined by the equations α m = a 0 exp[zg(v-v 1/2 )F]/RT β m = b 0 exp[-z(1-g)(v-v 1/2 )F]/RT where F is the Faraday constant, R is the gas constant and T is temperature. The kinetics of each channel was determined by the values assigned to the parameters a 0,b 0,z,g and V 1/2. A similar set of equations governed the inactivation variable, h, and its steady state value, h inf. The values of all the parameters used in the model are shown in Table 1. Results Dendritic saturation Dendrites have a much higher input impedance than the soma (Rinzel & Rall, 1974); thus even single EPSPs can produce significant local depolarization and reduce the driving force on simultaneous and subsequent EPSPs on the same dendritic branch. In addition, synaptic conductances add to the resting membrane conductance of the neuron (Barrett & Crill, 1974; Bernander et al., 1991; Holmes & Woody, 1989; Rapp et al., 1992) (see Methods). This effective decrease in R m and increase in λ also results in reduced

30 17 depolarizations for simultaneous and subsequent EPSPs. We refer to these two phenomena collectively as the dendritic saturation effect, although the term saturation does not necessarily imply that the membrane is at the synaptic reversal potential or that R m has been effectively reduced to zero. There is some direct experimental evidence for saturation during synaptic activation under physiological conditions. Ferster and Jagadeesh (1992) have demonstrated that the size of an EPSP evoked in visual cortical cells by electrical stimulation of the LGN was reduced during depolarizations caused by visual stimulation compared to its size at the resting potential. The reduction in EPSP size was proportional to the somatic depolarization caused by the visual stimulation. Thus, an EPSP that peaked at about 6 mv at rest was reduced to less than 1 mv when the cell was depolarized from a resting potential of -60 mv to a potential of -40 mv by visual stimulation (Fig. 3a) (Ferster & Jagadeesh, 1992). Ferster and Jagadeesh interpreted their results as evidence that the synaptic sites (dendrites) were significantly more depolarized than the soma during synaptic activation of the cell, thus producing saturation by the process described above. We have tested this hypothesis by simulating their experiment, and the results are shown in Figs. 2 and 3. The model layer 2 pyramidal cell was used because its morphology (Fig. 1) is reasonably close to that of the putative layer 4 spiny stellate cells that Ferster and Jagadeesh studied. A constant current of -0.1 na was injected starting at 30 ms to prevent firing during the synaptic activation, as in the experiments of Ferster and Jagadeesh. Visual stimulation was simulated by 70 excitatory synapses placed randomly on the basal/oblique dendrites, activated by a Poisson process at some mean frequency (for example, 50Hz) starting at 80 ms. 35 additional excitatory synapses were placed on the same dendritic segments as the initial 70, and were given a single simultaneous stimulation at 5 ms and again at 150 ms. The firing of these 35 synapses represented the effects of electrical stimulation of the

31 18 LGN: the first stimulation gave a control EPSP, the second, occurring during visual stimulation, gave a test EPSP. Different trials using a different seed for the random number generator produced Poisson-distributed trains of EPSPs. One such trial is shown in Fig. 2 (upper trace). The test EPSP was significantly reduced with respect to the control EPSP (by 34% in this case). Effects of spines The saturation effect underlying the reduction in EPSP amplitude was dependent on the membrane potential at the synaptic site. Excitatory synapses on real pyramidal cells are made onto spines, not onto dendritic shafts. It was conceivable that the small dimensions, and hence higher input resistance, of a spine head relative to that of a dendritic shaft might lead to greater saturation effects for EPSPs on spines vs. shafts (Segev & Rall, 1988). Consequently, we performed some simulations with excitatory synapses on spine heads rather than dendritic shafts. For a single 0.5 ns EPSP, there was very little difference in the depolarization recorded at the soma for a synapse on the head of a spine vs. on the dendritic shaft; the activation of synapses on spines produced a somatic peak amplitude more than 90% of that from synapses on the shaft. Significant saturation of single EPSPs due to the passive properties of the spine (Douglas & Martin, 1990b) was only observed if the peak EPSP conductance was increased to several ns. EPSPs produced by these conductance changes were larger than those typically observed in neocortical pyramidal cells (Mason et al., 1991). To simulate the experiment of Ferster and Jagadeesh with spines explicitly included, 70 spines were placed on the 70 basal dendritic compartments chosen above, then 35 more were added to provide the control and test EPSPs. The result of the

32 19 simulation with all excitatory synapses on spines (lower trace, Fig. 2) was not significantly different from that with all excitatory synapses directly on dendritic shafts (upper trace). The presence of spines did not make a difference over the full range of visual stimulation frequencies used. We also found very little difference between simulations using ns test synapses and those using ns test synapses. Although spines may be of great significance in some contexts (Zador et al., 1990), we were only concerned here with ensuring that our results would not be significantly affected by placing all the excitatory synapses on dendritic shafts rather than on spine heads. Fig. 2 shows that this approach is justfied. For this reason, in the remaining simulations spines were not included. Effect of excitation on saturation Fig. 3b shows the results of multiple trials at different frequencies of visual stimulation. Higher frequencies of excitatory input produced greater somatic depolarization, as would occur in a cell as the visual stimulus was presented at increasingly optimal values of orientation, velocity and direction. The peak amplitude of the EPSP is plotted against the somatic membrane potential (Vm) just before the EPSP occurs. As in the experimental data (Fig. 3a), the amplitude of the evoked EPSP decreased linearly with Vm. The dendrites were depolarized to between -25 mv and -20 mv during maximal synaptic activation, which means that the EPSP driving force was reduced by about 60%. Since the test EPSP was reduced by about 80% during maximal synaptic activation (Fig. 3b), a reduction in EPSP size of approximately 20% was due to a reduction in R in caused by the excitatory synaptic input. A more detailed, quantitative description of changes in R in during synaptic activation is presented in the last section of the results.

33 20 The results shown in Fig. 3b provide a qualitative match to those of Ferster and Jagadeesh, but the difference between the level of somatic and dendritic depolarization in the model was not great. In addition, the slope of the relationship between EPSP height and somatic Vm was not as steep as in the experimental data: the abscissa intercept (EPSP reduced to 0 mv) is about -40 mv in the experimental results (Fig. 3a) and -25 mv in Fig. 3b. Ferster and Jagadeesh report that visual cortical cells cannot be depolarized by more than 20 mv from rest by visual stimulation (Ferster & Jagadeesh, 1992). For our model cell (resting potential -65 mv), this corresponds to complete saturation at a somatic Vm of -45 mv. Effect of inhibition on saturation The difference between our simulations of dendritic saturation and the experimental results could be due to the omission of inhibitory input in the simulation. Recent studies (Berman et al., 1991; Douglas et al., 1988; Ferster & Jagadeesh, 1992) have indicated that inhibitory input to visual cortical cells is weak during nonpreferred responses and is strongly correlated with the degree of activation of the excitatory cells (Ferster, 1986; Somers et al., 1993). This fits with anatomical evidence that spiny excitatory cells make direct contacts with inhibitory cells, which then make direct contacts back onto the same excitatory population (Douglas & Martin, 1991). We repeated the simulation described above, this time including 33 inhibitory synapses, 12 on the soma and 21 on the preterminal basal/oblique dendrites. This is the pattern of innervation characteristic of basket cells, the most common inhibitory cell type in cortex (Martin, 1988). Inhibitory (smooth) cells fire at much higher rates than pyramidal cells (McCormick et al., 1985); therefore, inhibitory synapses were activated at a mean frequency twice that of the excitatory synapses. Fig. 3c shows the results of including inhibition in the

34 21 simulation. The EPSP/somatic V m slope is steeper, with an abscissa intercept of about -35 mv. This is much closer to the experimental data of Ferster and Jagadeesh (Fig. 3a). Dendrites were depolarized to about -30 mv during maximal synaptic activation, less than in the excitation-alone case, yet the EPSP/somatic V m slope is steeper with inhibition. A dendritic depolarization to around -30 mv reduced the EPSP driving force by about 50%. Test EPSPs were reduced in amplitude by up to 80%, so the remaining 30% must be due to decreases in R in caused by the excitatory and inhibitory synaptic conductance changes (see Discussion). There may also be some contribution to the reduction in R in and hence EPSP amplitude from intrinsic sub-threshold voltage-dependent conductances during the experiments of Ferster and Jagadeesh. The simulations of Fig. 3 did not include voltagedependent conductances, so we cannot evaluate the extent of this contribution, but the simulations of Bernander et al. (1991) indicate that it is likely to be relatively small. Ferster and Jagadeesh (1992) focused on reduction in driving force as the explanation for the decreases in evoked EPSP amplitude that they observed, but we found that decreases in R in (decrease in effective R m ) due to excitatory inputs made a significant contribution. Furthermore, additional current shunts due to inhibitory synaptic activity must be included to produce an accurate fit to the experimental data. The data in Fig. 3c fall along a straight line because the major component of the saturation effect is due to the linear reduction in driving force. The contribution from increased membrane conductance, which would produce a concave (hyperbolic) curve, is masked by the driving force effect and the variance in the data. When inhibition was included in the simulation the soma could not be depolarized past -45 mv by the firing of the 70 excitatory synapses, which is the limit of depolarization obtainable with optimal visual stimulation reported by Ferster and Jagadeesh (1992).

35 22 Fig. 3d shows that the decrease in test EPSP amplitude due to dendritic saturation is stable across a wide range of values for R m and R i. The rate of decrease of EPSP amplitude with somatic V m was constant over the full parameter range. Fig. 4 displays in higher resolution dendritic (dashed lines) and somatic (solid lines) membrane potentials at the time of the test EPSP (arrow) for synaptic input with (lower traces) and without (upper traces) inhibition. A number of important points are illustrated: Because of a higher Rin, the dendrite is more depolarized than the soma (and this dendrite is less depolarized than most), with larger voltage fluctuations due to the influence of individual PSPs. The dendrite is less hyperpolarized than the soma by the inhibition because the inhibitory synapses are proximal and act by shunting current that passes from the dendrites to the soma. The effect of inhibition is to increase the slope of the test EPSP/somatic Vm graph (Fig. 3c), so at the low input rate shown here inhibition causes a small increase in the size of the test EPSP by slightly hyperpolarizing the membrane thus increasing the excitatory synaptic driving force. GABAA inhibition, the type we are modelling here, acts by increasing membrane conductance rather than directly hyperpolarizing the membrane, as its reversal potential is close to the resting membrane potential. The driving force for inhibitory chloride conductance only exists when there is depolarization produced by excitatory synaptic input (silent inhibition). At higher firing rates, when the inhibitory conductance is large, the small increase in excitatory driving force caused by the hyperpolarization, (which is minimised at the site of the excitatory synapses by the spatial separation of the sources of excitatory and inhibitory input, mentioned above) is more than offset by the shunting effect of the inhibition and the test EPSP is decreased in size (Fig. 3c). The soma could still be depolarized by 20 mv from rest even when the 33 inhibitory synapses are firing at their maximum rate (Fig. 3). This indicates that firing of the postsynaptic cell would persist despite significant inhibition. This seems to support the